nLab symmetric topos

Idea

The symmetric topos $M(\mathcal{E})$ of a Grothendieck topos $\mathcal{E}$ is the topos analogue of the symmetric algebra construction. Its importance stems from the property that for a topos $\mathcal{E}$ the symmetric topos $M(\mathcal{E})$ classifies topos distributions on $\mathcal{E}$.

Definition

Properties

Example

Related entries

• Lawvere distribution

• bagdomain topos

• cosheaf

• locally connected geometric morphism

• totally connected geometric morphism

• lax-idempotent 2-monad

References

• Marta Bunge, Cosheaves and Distributions on Toposes , Alg. Univ. 34 (1995) pp.469-484.

• Marta Bunge, Aurelio Carboni, The Symmetric Topos , JPAA 105 (1995) pp.233-249.

• Marta Bunge, Jonathon Funk, Spreads and the Symmetric Topos , JPAA 113 (1996) pp.1-38.

• Marta Bunge, Jonathon Funk, Spreads and the Symmetric Topos II , JPAA 130 (1998) pp.49-84.

• Marta Bunge, Jonathon Funk, On a bicomma object condition for KZ-doctrines , JPAA 143 (1999) pp.69-105.

• Marta Bunge, Jonathon Funk, Singular Coverings of Toposes , Springer LNM 1890 Heidelberg 2006.

• Peter Johnstone, Sketches of an Elephant I , Oxford UP 2002. (sec. B4.5, pp.456-467)

• Andrew M. Pitts, On product and change of base for toposes , Cah. Top. Géom. Diff. Cat. XXVI no.1 (1985) pp.43-61.

• Steve Vickers, Cosheaves and Connectedness in Formal Topology , Ann. Pure Appl. Logic 163 no.2 (2012) pp.157-174. (preprint)